I'm working for an outsourcing company that is managing the infrastructure (servers and DBs) for one of its clients. However, all the applications are supported by the client.
In this mixed environment, sometimes the application support teams need to raise a change where infrastructure have multiple tasks. The application team will raise and 'own' the change and coordinate all the activities assigned to each team.
On the other hand, there are metrics in place for the Change Process and particularly, for failed changes.
The problem is that when one of such 'mixed' changes fails, it's hard to determine who should 'wear' it (in their metrics). Should it be the team that owns the change? Or the team whose task failed?
This topic is becoming really hard to handle as there is a commercial agreement in place and reporting on change activity.

I would suggest that the metrics put in place were theoretical rather than in reference to anything useful you need to measure. It's all back to definitions and contractual agreements.

A metric for changes failed measures change management.

A measure for changes failed due to poor testing measures test management.

A metric for change failed due to network staff error measures network management.

If different parties have different scope and responsibility you need to set up measures that cover their scope and responsibility.

If you do it on an ad hoc basis (analysing each change as it fails and debating where the cause is) then everyone will argue with one eye on the contract and very little care for reality. So, to fix your problem you need to go back to the contract (mutually) and design a set of metrics that will address the constraints of the contract.

Nothing could be easier

I'd just like to add that, for everyone who ever asks for a list of "good metrics" or "standard metrics", this is a prime reason why they won't work for you. They might sound good and look good but they are not mapped to your service._________________"Method goes far to prevent trouble in business: for it makes the task easy, hinders confusion, saves abundance of time, and instructs those that have business depending, both what to do and what to hope."
William Penn 1644-1718